Question

Jessica has a normal deck of cards, which contains 52 cards. She asks her friend Sarah to draw a card. What are the odds in favor of Sarah selecting the queen of hearts? What are the odds against Sara selecting the queen of hearts?

Answer 1

Given :- Jessica has a normal deck of cards, which contains 52 cards. She asks her friend Sarah to draw a card. What are the odds in favor of Sarah selecting the queen of hearts ? What are the odds against Sara selecting the queen of hearts ?

Solution :-

→ Total cards = 52 = Total number of outcomes .

and,

→ selecting a queen of hearts = only 1 in the deck = Total favourable outcomes .

so,

→ Total unfavourable outcomes = Total number of outcomes - Total favourable outcomes = 52 - 1 = 51

then,

→ The odds in favor of sarah selecting the queen of hearts = Total favourable outcomes / Total unfavourable outcomes = (1/51) = 1 : 51 (Ans.)

and,

→ The odds against sarah selecting the queen of hearts = Total unfavourable outcomes / Total favourable outcomes= (51/1) = 51 : 1 (Ans.)

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Answer 2

Given:

Jessica has a normal deck of cards, which contains 52 cards. She asks her friend Sarah to draw a card.

To find:

• What are the odds in favor of Sarah selecting the queen of hearts?
• What are the odds against Sara selecting the queen of hearts?

Solution:

• The deck of cards contains 52 cards in which there is only 1 queen of hearts.
• ''Queen of hearts'' is a ''favorable outcome''.
• ''All other cards'' are an ''unfavorable outcome''.

The odds in favor of Sarah selecting the queen of hearts:

$=> \dfrac{favorable \: outcomes}{unfavorable \: outcomes} =\dfrac{1}{51}$

$Ratio \: is => 1 : 51$

The odds against Sara selecting the queen of hearts:

$=> \dfrac{unfavorable \: outcomes}{favorable \: outcomes} =\dfrac{51}{1}$

$Ratio \: is => 51 : 1$